Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
0 votes
312 views
in Physics by (115k points)

A rocket of length 5 meters passes an observer on earth. The observer measures the passing rocket to be 3 meters long. What is the velocity of the rocket in the reference frame of the Earth-based observer?


1. 0.6c
2. 1.25c
3. 0.8c
4. 0.4c

1 Answer

0 votes
by (114k points)
selected by
 
Best answer
Correct Answer - Option 3 : 0.8c

Concept:

If we measure the length of anything moving relative to our frame, we find its length L to be smaller than the proper length L0 that would be measured if the object were stationary. 

At relativistic speeds, Close to the speed of light, distances measured are not the same when measured by different observers.

Length Contraction:

Length contraction is the decrease in the measured length of an object from its proper length when measured in a reference frame that is moving with respect to the object.

It is given by 

\(L = {L_0}\sqrt {1 - \frac{{{v^2}}}{{{c^2}}}} \)

where L0 is the length of the object in its rest frame, and L is the length in the frame moving with velocity v;

Calculation:

Given:

L0 = 5 m and L = 3 cm

Using, \(L = {L_0}\sqrt {1 - \frac{{{v^2}}}{{{c^2}}}} \)

⇒  \(3 = 5\sqrt {1 - \frac{{{v^2}}}{{{c^2}}}} \)

⇒ \(1-\frac{9}{{25}} =\frac{{{v^2}}}{{{c^2}}}\)

⇒ \(\frac{{{v^2}}}{{{c^2}}} =\frac{{16}}{{25}} \)

\(\frac{v}{c}=\frac{4}{5}\)

v = 0.8c

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

Categories

...